%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU550^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:28 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 2
% Syntax : Number of formulae : 78 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 269 ( 89 equ; 0 cnn)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 600 ( 99 ~; 172 |; 13 &; 300 @)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 99 ( 6 ^; 89 !; 4 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
epred1_0: $i > $o ).
thf(decl_25,type,
epred2_0: $i > $o ).
thf(decl_26,type,
esk1_1: $i > $i ).
thf(decl_27,type,
esk2_1: $i > $i ).
thf(decl_28,type,
esk3_0: $i ).
thf(decl_29,type,
esk4_0: $i ).
thf(exu__Cong,conjecture,
! [X1: $i > $o,X4: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X4 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X4 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ILvDBUylR2/E---3.1_133650.p',exu__Cong) ).
thf(exu_def,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ILvDBUylR2/E---3.1_133650.p',exu_def) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: $i > $o,X4: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X4 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
<=> ( exu
@ ^ [X2: $i] : ( X4 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[exu__Cong]) ).
thf(c_0_3,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu_def]) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i > $o,X4: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X4 @ X3 ) ) )
=> ( ? [X9: $i] :
( ( X1 @ X9 )
& ! [X10: $i] :
( ( X1 @ X10 )
=> ( X9 = X10 ) ) )
<=> ? [X11: $i] :
( ( X4 @ X11 )
& ! [X12: $i] :
( ( X4 @ X12 )
=> ( X11 = X12 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2]),c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X15: $i,X16: $i,X17: $i,X19: $i,X22: $i,X24: $i] :
( ( ~ ( epred1_0 @ X15 )
| ( epred2_0 @ X16 )
| ( X15 != X16 ) )
& ( ~ ( epred2_0 @ X16 )
| ( epred1_0 @ X15 )
| ( X15 != X16 ) )
& ( ( epred2_0 @ ( esk2_1 @ X19 ) )
| ~ ( epred2_0 @ X19 )
| ( epred1_0 @ ( esk1_1 @ X17 ) )
| ~ ( epred1_0 @ X17 ) )
& ( ( X19
!= ( esk2_1 @ X19 ) )
| ~ ( epred2_0 @ X19 )
| ( epred1_0 @ ( esk1_1 @ X17 ) )
| ~ ( epred1_0 @ X17 ) )
& ( ( epred2_0 @ ( esk2_1 @ X19 ) )
| ~ ( epred2_0 @ X19 )
| ( X17
!= ( esk1_1 @ X17 ) )
| ~ ( epred1_0 @ X17 ) )
& ( ( X19
!= ( esk2_1 @ X19 ) )
| ~ ( epred2_0 @ X19 )
| ( X17
!= ( esk1_1 @ X17 ) )
| ~ ( epred1_0 @ X17 ) )
& ( ( epred2_0 @ esk4_0 )
| ( epred1_0 @ esk3_0 ) )
& ( ~ ( epred2_0 @ X24 )
| ( esk4_0 = X24 )
| ( epred1_0 @ esk3_0 ) )
& ( ( epred2_0 @ esk4_0 )
| ~ ( epred1_0 @ X22 )
| ( esk3_0 = X22 ) )
& ( ~ ( epred2_0 @ X24 )
| ( esk4_0 = X24 )
| ~ ( epred1_0 @ X22 )
| ( esk3_0 = X22 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i,X2: $i] :
( ( epred1_0 @ X3 )
| ~ ( epred2_0 @ X2 )
| ( X3 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(er,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( epred2_0 @ esk4_0 )
| ( epred1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i,X3: $i] :
( ( epred2_0 @ ( esk2_1 @ X2 ) )
| ( epred1_0 @ ( esk1_1 @ X3 ) )
| ~ ( epred2_0 @ X2 )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
( ( epred1_0 @ esk3_0 )
| ( epred1_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk1_1 @ esk3_0 ) )
| ( epred2_0 @ ( esk2_1 @ X2 ) )
| ( epred1_0 @ esk4_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X2: $i,X3: $i] :
( ( epred2_0 @ X3 )
| ~ ( epred1_0 @ X2 )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ esk4_0 )
| ( esk3_0 = X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk1_1 @ esk3_0 ) )
| ( epred1_0 @ ( esk2_1 @ X2 ) )
| ( epred1_0 @ esk4_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(er,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk3_0 )
| ( epred1_0 @ ( esk1_1 @ esk3_0 ) )
| ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk3_0 )
| ( epred1_0 @ ( esk1_1 @ esk3_0 ) )
| ( epred2_0 @ esk4_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_18,negated_conjecture,
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( epred1_0 @ ( esk1_1 @ esk3_0 ) )
| ( epred2_0 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X2: $i,X3: $i] :
( ( epred1_0 @ ( esk1_1 @ X3 ) )
| ( X2
!= ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_20,negated_conjecture,
( ( ( esk2_1 @ esk3_0 )
= esk3_0 )
| ( ( esk1_1 @ esk3_0 )
= esk3_0 )
| ( epred2_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i] :
( ( ( esk1_1 @ esk3_0 )
= esk3_0 )
| ( epred1_0 @ ( esk1_1 @ X2 ) )
| ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,negated_conjecture,
! [X2: $i] :
( ( ( esk1_1 @ esk3_0 )
= esk3_0 )
| ( ( esk1_1 @ X2 )
= esk3_0 )
| ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X2: $i] :
( ( ( esk1_1 @ esk3_0 )
= esk3_0 )
| ( ( esk1_1 @ X2 )
= esk3_0 )
| ( epred2_0 @ esk4_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_8]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i,X3: $i] :
( ( epred2_0 @ ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 )
| ( X3
!= ( esk1_1 @ X3 ) )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_25,negated_conjecture,
( ( ( esk1_1 @ esk3_0 )
= esk3_0 )
| ( epred2_0 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_10]),c_0_15]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ ( esk2_1 @ X2 ) )
| ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_8]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk2_1 @ X2 ) )
| ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_26]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk3_0 )
| ( epred2_0 @ esk4_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
thf(c_0_29,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i,X3: $i] :
( ( X2
!= ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 )
| ( X3
!= ( esk1_1 @ X3 ) )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_31,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk4_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
thf(c_0_32,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ esk4_0 )
| ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_8]) ).
thf(c_0_33,negated_conjecture,
( ( epred2_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_10]),c_0_15]) ).
thf(c_0_34,negated_conjecture,
epred2_0 @ esk4_0,
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28])]),c_0_33]) ).
thf(c_0_35,negated_conjecture,
epred1_0 @ esk4_0,
inference(spm,[status(thm)],[c_0_7,c_0_34]) ).
thf(c_0_36,negated_conjecture,
! [X2: $i] :
( ( esk4_0 = X2 )
| ( epred1_0 @ esk3_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_37,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ( epred2_0 @ ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_35]) ).
thf(c_0_38,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ( epred1_0 @ esk3_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_39,negated_conjecture,
! [X2: $i] :
( ( esk4_0 = X2 )
| ( epred1_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_15]) ).
thf(c_0_40,negated_conjecture,
( ( ( esk2_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ( epred1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_34]) ).
thf(c_0_41,negated_conjecture,
( ( ( esk2_1 @ esk4_0 )
= esk4_0 )
| ( ( esk1_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_42,negated_conjecture,
! [X2: $i] :
( ( ( esk1_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ X2 ) )
| ( epred1_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_41]),c_0_34])]) ).
thf(c_0_43,negated_conjecture,
! [X2: $i] :
( ( ( esk1_1 @ esk4_0 )
= esk4_0 )
| ( ( esk1_1 @ X2 )
= esk4_0 )
| ( epred1_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
thf(c_0_44,negated_conjecture,
( ( ( esk1_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
thf(c_0_45,negated_conjecture,
! [X2: $i,X3: $i] :
( ( esk4_0 = X2 )
| ( esk3_0 = X3 )
| ~ ( epred2_0 @ X2 )
| ~ ( epred1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_46,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ ( esk2_1 @ X2 ) )
| ( epred1_0 @ esk3_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_44]),c_0_35])]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i] :
( ( esk3_0 = esk4_0 )
| ( esk4_0 = X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_35]) ).
thf(c_0_48,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ esk3_0 )
| ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_44]),c_0_35])]) ).
thf(c_0_49,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( epred1_0 @ esk3_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_46]) ).
thf(c_0_50,negated_conjecture,
! [X2: $i] :
( ( esk3_0 = esk4_0 )
| ( esk4_0 = X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_15]) ).
thf(c_0_51,negated_conjecture,
epred1_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49])]),c_0_34])]) ).
thf(c_0_52,negated_conjecture,
esk3_0 = esk4_0,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_53,negated_conjecture,
! [X2: $i,X3: $i] :
( ( esk4_0 = X2 )
| ( esk4_0 = X3 )
| ~ ( epred1_0 @ X2 )
| ~ ( epred2_0 @ X3 ) ),
inference(rw,[status(thm)],[c_0_45,c_0_52]) ).
thf(c_0_54,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ( epred1_0 @ ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_37]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( esk4_0 = X3 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ~ ( epred2_0 @ X3 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_56,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( ( esk2_1 @ X3 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ~ ( epred2_0 @ X3 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_37]) ).
thf(c_0_57,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( esk2_1 @ ( esk2_1 @ X2 ) )
= esk4_0 )
| ( ( esk2_1 @ X3 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ~ ( epred2_0 @ X3 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_37]) ).
thf(c_0_58,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( esk2_1 @ ( esk2_1 @ X2 ) )
= esk4_0 )
| ( ( esk2_1 @ X3 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ~ ( epred2_0 @ X2 )
| ~ ( epred1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_15]) ).
thf(c_0_59,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ ( esk2_1 @ esk4_0 ) )
= esk4_0 )
| ( ( esk2_1 @ X2 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_34]) ).
thf(c_0_60,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ ( esk2_1 @ esk4_0 ) )
= esk4_0 )
| ( ( esk2_1 @ ( esk2_1 @ X2 ) )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_54]) ).
thf(c_0_61,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk4_0 )
= esk4_0 )
| ( ( esk2_1 @ X2 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_56,c_0_34]) ).
thf(c_0_62,negated_conjecture,
( ( ( esk2_1 @ ( esk2_1 @ esk4_0 ) )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_60,c_0_34]) ).
thf(c_0_63,negated_conjecture,
( ( ( esk2_1 @ esk4_0 )
= esk4_0 )
| ( epred1_0 @ ( esk1_1 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_61,c_0_34]) ).
thf(c_0_64,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ( epred1_0 @ ( esk1_1 @ X2 ) )
| ~ ( epred2_0 @ ( esk2_1 @ esk4_0 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_62]),c_0_63]) ).
thf(c_0_65,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk1_1 @ esk4_0 ) )
| ( epred1_0 @ ( esk1_1 @ X2 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_37]),c_0_34])]) ).
thf(c_0_66,negated_conjecture,
epred1_0 @ ( esk1_1 @ esk4_0 ),
inference(spm,[status(thm)],[c_0_65,c_0_35]) ).
thf(c_0_67,negated_conjecture,
! [X2: $i] :
( ( ( esk1_1 @ esk4_0 )
= esk4_0 )
| ( esk4_0 = X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_66]) ).
thf(c_0_68,negated_conjecture,
! [X2: $i] :
( ( ( esk1_1 @ esk4_0 )
= esk4_0 )
| ( esk4_0 = X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_15]) ).
thf(c_0_69,negated_conjecture,
( ( esk1_1 @ esk4_0 )
= esk4_0 ),
inference(spm,[status(thm)],[c_0_68,c_0_66]) ).
thf(c_0_70,negated_conjecture,
! [X2: $i] :
( ( epred2_0 @ ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_69]),c_0_35])]) ).
thf(c_0_71,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ ( esk2_1 @ X2 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_70]) ).
thf(c_0_72,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( esk4_0 = X3 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_71]) ).
thf(c_0_73,negated_conjecture,
! [X3: $i,X2: $i] :
( ( ( esk2_1 @ X2 )
= esk4_0 )
| ( ( esk2_1 @ X3 )
= esk4_0 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_70]) ).
thf(c_0_74,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ esk4_0 )
= esk4_0 )
| ( ( esk2_1 @ X2 )
= esk4_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_34]) ).
thf(c_0_75,negated_conjecture,
! [X2: $i] :
( ( ( esk2_1 @ X2 )
!= X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_69]),c_0_35])]) ).
thf(c_0_76,negated_conjecture,
( ( esk2_1 @ esk4_0 )
= esk4_0 ),
inference(spm,[status(thm)],[c_0_74,c_0_34]) ).
thf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU550^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:49:18 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.13 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ILvDBUylR2/E---3.1_133650.p
% 0.08/0.16 % Version: 3.5.1-ho
% 0.08/0.16 % Preprocessing class: HSSSSMSSSLMNHSA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.16 % new_bool_1 with pid 133666 completed with status 0
% 0.08/0.16 % Result found by new_bool_1
% 0.08/0.16 % Preprocessing class: HSSSSMSSSLMNHSA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.16 % Search class: HGHSF-FFSF11-SHSFMFNN
% 0.08/0.16 % partial match(1): HHHSF-FFSF11-SHSFMFNN
% 0.08/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.16 % SubtermCWHack with pid 133670 completed with status 0
% 0.08/0.16 % Result found by SubtermCWHack
% 0.08/0.16 % Preprocessing class: HSSSSMSSSLMNHSA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.16 % Search class: HGHSF-FFSF11-SHSFMFNN
% 0.08/0.16 % partial match(1): HHHSF-FFSF11-SHSFMFNN
% 0.08/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.16 % Preprocessing time : 0.001 s
% 0.08/0.16
% 0.08/0.16 % Proof found!
% 0.08/0.16 % SZS status Theorem
% 0.08/0.16 % SZS output start CNFRefutation
% See solution above
% 0.08/0.16 % Parsed axioms : 3
% 0.08/0.16 % Removed by relevancy pruning/SinE : 1
% 0.08/0.16 % Initial clauses : 10
% 0.08/0.16 % Removed in clause preprocessing : 0
% 0.08/0.16 % Initial clauses in saturation : 10
% 0.08/0.16 % Processed clauses : 203
% 0.08/0.16 % ...of these trivial : 3
% 0.08/0.16 % ...subsumed : 62
% 0.08/0.16 % ...remaining for further processing : 138
% 0.08/0.16 % Other redundant clauses eliminated : 8
% 0.08/0.16 % Clauses deleted for lack of memory : 0
% 0.08/0.16 % Backward-subsumed : 40
% 0.08/0.16 % Backward-rewritten : 79
% 0.08/0.16 % Generated clauses : 698
% 0.08/0.16 % ...of the previous two non-redundant : 622
% 0.08/0.16 % ...aggressively subsumed : 0
% 0.08/0.16 % Contextual simplify-reflections : 16
% 0.08/0.16 % Paramodulations : 689
% 0.08/0.16 % Factorizations : 1
% 0.08/0.16 % NegExts : 0
% 0.08/0.16 % Equation resolutions : 8
% 0.08/0.16 % Disequality decompositions : 0
% 0.08/0.16 % Total rewrite steps : 300
% 0.08/0.16 % ...of those cached : 293
% 0.08/0.16 % Propositional unsat checks : 0
% 0.08/0.16 % Propositional check models : 0
% 0.08/0.16 % Propositional check unsatisfiable : 0
% 0.08/0.16 % Propositional clauses : 0
% 0.08/0.16 % Propositional clauses after purity: 0
% 0.08/0.16 % Propositional unsat core size : 0
% 0.08/0.16 % Propositional preprocessing time : 0.000
% 0.08/0.16 % Propositional encoding time : 0.000
% 0.08/0.16 % Propositional solver time : 0.000
% 0.08/0.16 % Success case prop preproc time : 0.000
% 0.08/0.16 % Success case prop encoding time : 0.000
% 0.08/0.16 % Success case prop solver time : 0.000
% 0.08/0.16 % Current number of processed clauses : 17
% 0.08/0.16 % Positive orientable unit clauses : 5
% 0.08/0.16 % Positive unorientable unit clauses: 0
% 0.08/0.16 % Negative unit clauses : 0
% 0.08/0.16 % Non-unit-clauses : 12
% 0.08/0.16 % Current number of unprocessed clauses: 204
% 0.08/0.16 % ...number of literals in the above : 1054
% 0.08/0.16 % Current number of archived formulas : 0
% 0.08/0.16 % Current number of archived clauses : 119
% 0.08/0.16 % Clause-clause subsumption calls (NU) : 1417
% 0.08/0.16 % Rec. Clause-clause subsumption calls : 685
% 0.08/0.16 % Non-unit clause-clause subsumptions : 116
% 0.08/0.16 % Unit Clause-clause subsumption calls : 57
% 0.08/0.16 % Rewrite failures with RHS unbound : 0
% 0.08/0.16 % BW rewrite match attempts : 7
% 0.08/0.16 % BW rewrite match successes : 7
% 0.08/0.16 % Condensation attempts : 0
% 0.08/0.16 % Condensation successes : 0
% 0.08/0.16 % Termbank termtop insertions : 11939
% 0.08/0.16 % Search garbage collected termcells : 417
% 0.08/0.16
% 0.08/0.16 % -------------------------------------------------
% 0.08/0.16 % User time : 0.012 s
% 0.08/0.16 % System time : 0.002 s
% 0.08/0.16 % Total time : 0.014 s
% 0.08/0.16 % Maximum resident set size: 3632 pages
% 0.08/0.16
% 0.08/0.16 % -------------------------------------------------
% 0.08/0.16 % User time : 0.013 s
% 0.08/0.16 % System time : 0.005 s
% 0.08/0.16 % Total time : 0.017 s
% 0.08/0.16 % Maximum resident set size: 4864 pages
% 0.08/0.16 % E exiting
%------------------------------------------------------------------------------